The simplest explanation is that the needle aligns itself with the direction of the magnetic field lines. Since the lines are perpendicular to the direction of current, the needle will try to align that way also. It is only deflected west because Earth's magnetic field is still pulling the needle to point north. The needle will point along the resultant vector.
A pretty good explanation can be found here, which is probably a bit more in-depth than I was, although not all of it relates directly to the fields of current carrying wires.
This should be simple enough to test with a wire and a couple of 9-volt batteries. If you try this, be careful not to short the batteries because shorted batteries can be dangerous.